//2009/07/27 15:56:44
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>

using namespace std;

class FixedPointTheorem
{
public:
    double cycleRange(double R)
    {
		double x = 0.25;
		double min = 999999.00;
		double max = -999999.00;
		for(int i=0; i<=201000; i++)
		{
			x = R * x * (1-x);
			if(i >= 200001)
			{
				if(x > max)
					max = x;
				if(x < min)
					min = x;
			}
		}
		return max-min;
    }
};
